Atomistic study of surface effects in metals

Atomistic simulations are a useful way to study nanoscale metal structures. At the nanoscale, the surface to volume ratio of the objects becomes large and surface effects start to play a critically important role. The internal stress near a surface can reach the GPa range and thus its effects should not be neglected when dealing with nanowires and other nanostructures. Similarly, surface diffusion of atoms is important in the manufacturing process and subsequent stability of nanostructures. In the study of vacuum breakdown on Cu surfaces, dislocation activity and surface atom diffusion are thought to play a role in the formation of field enhancing emitters. This work investigates a possible mechanism of nucleation of a nanofeature on metal surfaces under high electric fields in the presence of a near-surface defect, and the stability of Au nanowires with respect to surface diffusion. The simulation methods of molecular dynamics, kinetic Monte Carlo and finite elements are employed. A subsurface Fe precipitate is used as an example of subsurface extended defects, and the nucleation of dislocations in regions of high stress concentration is simulated. A process of forming a protrusion on the surface near the precipitate due to dislocation propagation is shown, as well as the possibility of forming new voids on the precipitate interface. Since atomistic simulations are heavily limited in size and time scales, larger scale simulations are conducted by using finite element modelling of nanoscale material behavior under external loading. However, such modeling requires the development of an accurate model of surface stress. In this work, a surface stress model is implemented into a continuum finite element model to enable faster calculations of more extensive nanoscale systems, as well as to combine the mechanical model with electrical effects in vacuum breakdown research. The internal stresses given by the model are validated in comparison with molecular dynamics simulations and against an analytical model of dislocation emission from a near-surface void. Kinetic Monte Carlo simulation is a suitable tool to simulate diffusion processes. However, setting up KMC simulations requires a parametrization of atomic migration barriers. A consistent parametrization scheme, called the tethering method, is developed in the current work. The tethering method provides a robust automatic process to calculate migration barriers for on-lattice diffusion simulations. It allows the calculation of barriers for unstable processes, while having a minimal effect on stable barriers. The tethering method is used to create a parametrization for Au, which is used to simulate nanowire junction fragmentation. Nanowire junctions break up in a process similar to Rayleigh instability. In conjunction with experiments, it is shown that junctions fragment at a low temperature when nanowires themselves remain whole. Simulations demonstrate that the breakup can be explained by surface energy minimization due to atom diffusion and that the formation of a fragment at the nanowire crossing point is very reliable.Atomistiset simulaatiot ovat erinomainen tapa tutkia nanokokoisia metallirakenteita. Nanomittakaavassa pinta-alan suhde tilavuuteen on suuri, ja pinnalla tapahtuvat ilmiöt ovat hyvin merkittävässä roolissa. Sisäinen jännitys lähellä pintaa voi olla useita gigapascaleita, joten sen merkitys on huomioitava nanojohtimia ja muita nanorakenteita tutkittaessa. Myös atomien pintadiffuusio on tärkeä ilmiö nanorakenteiden valmistuksen ja vakauden kannalta. Kuparipinnalla tapahtuvien tyhjiövalokaarien tutkimuksessa dislokaatioiden liikkeen ja pinta-atomien diffusion arvellaan vaikuttavan sähkökenttää vahvistavien emitterien muodostumiseen. Tässä työssä tutkitaan nanomuodostelmien nukleaation mekanismia pintadefektien läheisyydessä voimakkaassa sähkökentässä, ja kultananojohtimien vakautta pintadiffuusion suhteen. Tutkimuksessa käytetään molekyylidynaamisia simulaatioita, kineettistä Monte Carloa ja elementtimenetelmää. Pinnanalaista rautasaostumaa käytetään esimerkkitapauksena pinnan alle ulottuvista defekteistä, ja korkean jännityksen alueilla tapahtuvaa dislokaatioiden nukleaatiota simuloidaan. Dislokaatioiden etenemisen näytetään aiheuttavan ulkonemien muodostumista pinnalla lähellä saostumaa. Myös uusien tyhjiöiden muodostumisen saostuman rajapinnalle näytetään olevan mahdollista. Koska atomististen simulaatioiden koko ja aikaskaala ovat hyvin rajallisia, suuremmat simulaatiot tehdään ulkoisen jännityksen alaisten nanomateriaalien elementtimallinnuksen avulla. Tällainen mallinnus kuitenkin vaatii tarkkaa mallia pintajännityksestä. Tässä työssä pintajännitysmalli toteutetaan jatkumoelementtimallissa, jotta suurempia nanosysteemejä voidaan simuloida nopeammin, ja jotta mekaaniset mallit saadaan yhdistettyä tyhjiövalokaaritutkimukseen. Mallin antamia sisäisen jännityksen arvoja verrataan molekyylidynaamisiin simulaatioihin ja pinnan lähellä sijaitsevan tyhiön emittoimien dislokaatioiden analyyttiseen malliin. Kineettinen Monte Carlo on hyvä työkalu diffuusioprosessien simuloimiseen. KMCsimulaatio kuitenkin vaatii parametreina atomististen siirtymien energiavalleja. Tämän työn osana kehitetään johdonmukainen parametrisointijärjestelmä, nimeltään liekamenetelmä. Tämän menetelmän avulla voidaan laskea hilassa tapahtuvien siirtymien energiavallit luotettavasti ja automaattisesti. Myös epävakaiden siirtymien energiavallien laskeminen mahdollistuu, ilman suurta vaikutusta vakaiden siirtymien energiavalleihin. Liekamenetelmällä luodaan parametrisaatio kultasysteemeille, jonka avulla simuloidaan risteävien nanojohtimien pirstoutumista. Nanojohtimien risteyskohdassa tapahtuva pirstoutuminen on Rayleigh’n epävakauden kaltainen prosessi. Yhdessä kokeellisten tutkimusten kanssa näytetään että risteyskohdat pirstoutuvat matalassa lämpötilassa, jossa yksittäiset nanojohtimet vielä pysyvät kokonaisina. Simulaatioiden perusteella pirstoutuminen voidaan selittää atomien diffuusion aiheuttamalla pintaenergian minimoitumisella. Risteyskohtaan muodostuu sirpale hyvin luotettavasti

Atomistic study of surface effects in metals

Atomistic simulations are a useful way to study nanoscale metal structures. At the nanoscale, the surface to volume ratio of the objects becomes large and surface effects start to play a critically important role. The internal stress near a surface can reach the GPa range and thus its effects should not be neglected when dealing with nanowires and other nanostructures. Similarly, surface diffusion of atoms is important in the manufacturing process and subsequent stability of nanostructures. In the study of vacuum breakdown on Cu surfaces, dislocation activity and surface atom diffusion are thought to play a role in the formation of field enhancing emitters. This work investigates a possible mechanism of nucleation of a nanofeature on metal surfaces under high electric fields in the presence of a near-surface defect, and the stability of Au nanowires with respect to surface diffusion. The simulation methods of molecular dynamics, kinetic Monte Carlo and finite elements are employed. A subsurface Fe precipitate is used as an example of subsurface extended defects, and the nucleation of dislocations in regions of high stress concentration is simulated. A process of forming a protrusion on the surface near the precipitate due to dislocation propagation is shown, as well as the possibility of forming new voids on the precipitate interface. Since atomistic simulations are heavily limited in size and time scales, larger scale simulations are conducted by using finite element modelling of nanoscale material behavior under external loading. However, such modeling requires the development of an accurate model of surface stress. In this work, a surface stress model is implemented into a continuum finite element model to enable faster calculations of more extensive nanoscale systems, as well as to combine the mechanical model with electrical effects in vacuum breakdown research. The internal stresses given by the model are validated in comparison with molecular dynamics simulations and against an analytical model of dislocation emission from a near-surface void. Kinetic Monte Carlo simulation is a suitable tool to simulate diffusion processes. However, setting up KMC simulations requires a parametrization of atomic migration barriers. A consistent parametrization scheme, called the tethering method, is developed in the current work. The tethering method provides a robust automatic process to calculate migration barriers for on-lattice diffusion simulations. It allows the calculation of barriers for unstable processes, while having a minimal effect on stable barriers. The tethering method is used to create a parametrization for Au, which is used to simulate nanowire junction fragmentation. Nanowire junctions break up in a process similar to Rayleigh instability. In conjunction with experiments, it is shown that junctions fragment at a low temperature when nanowires themselves remain whole. Simulations demonstrate that the breakup can be explained by surface energy minimization due to atom diffusion and that the formation of a fragment at the nanowire crossing point is very reliable.Atomistiset simulaatiot ovat erinomainen tapa tutkia nanokokoisia metallirakenteita. Nanomittakaavassa pinta-alan suhde tilavuuteen on suuri, ja pinnalla tapahtuvat ilmiöt ovat hyvin merkittävässä roolissa. Sisäinen jännitys lähellä pintaa voi olla useita gigapascaleita, joten sen merkitys on huomioitava nanojohtimia ja muita nanorakenteita tutkittaessa. Myös atomien pintadiffuusio on tärkeä ilmiö nanorakenteiden valmistuksen ja vakauden kannalta. Kuparipinnalla tapahtuvien tyhjiövalokaarien tutkimuksessa dislokaatioiden liikkeen ja pinta-atomien diffusion arvellaan vaikuttavan sähkökenttää vahvistavien emitterien muodostumiseen. Tässä työssä tutkitaan nanomuodostelmien nukleaation mekanismia pintadefektien läheisyydessä voimakkaassa sähkökentässä, ja kultananojohtimien vakautta pintadiffuusion suhteen. Tutkimuksessa käytetään molekyylidynaamisia simulaatioita, kineettistä Monte Carloa ja elementtimenetelmää. Pinnanalaista rautasaostumaa käytetään esimerkkitapauksena pinnan alle ulottuvista defekteistä, ja korkean jännityksen alueilla tapahtuvaa dislokaatioiden nukleaatiota simuloidaan. Dislokaatioiden etenemisen näytetään aiheuttavan ulkonemien muodostumista pinnalla lähellä saostumaa. Myös uusien tyhjiöiden muodostumisen saostuman rajapinnalle näytetään olevan mahdollista. Koska atomististen simulaatioiden koko ja aikaskaala ovat hyvin rajallisia, suuremmat simulaatiot tehdään ulkoisen jännityksen alaisten nanomateriaalien elementtimallinnuksen avulla. Tällainen mallinnus kuitenkin vaatii tarkkaa mallia pintajännityksestä. Tässä työssä pintajännitysmalli toteutetaan jatkumoelementtimallissa, jotta suurempia nanosysteemejä voidaan simuloida nopeammin, ja jotta mekaaniset mallit saadaan yhdistettyä tyhjiövalokaaritutkimukseen. Mallin antamia sisäisen jännityksen arvoja verrataan molekyylidynaamisiin simulaatioihin ja pinnan lähellä sijaitsevan tyhiön emittoimien dislokaatioiden analyyttiseen malliin. Kineettinen Monte Carlo on hyvä työkalu diffuusioprosessien simuloimiseen. KMCsimulaatio kuitenkin vaatii parametreina atomististen siirtymien energiavalleja. Tämän työn osana kehitetään johdonmukainen parametrisointijärjestelmä, nimeltään liekamenetelmä. Tämän menetelmän avulla voidaan laskea hilassa tapahtuvien siirtymien energiavallit luotettavasti ja automaattisesti. Myös epävakaiden siirtymien energiavallien laskeminen mahdollistuu, ilman suurta vaikutusta vakaiden siirtymien energiavalleihin. Liekamenetelmällä luodaan parametrisaatio kultasysteemeille, jonka avulla simuloidaan risteävien nanojohtimien pirstoutumista. Nanojohtimien risteyskohdassa tapahtuva pirstoutuminen on Rayleigh’n epävakauden kaltainen prosessi. Yhdessä kokeellisten tutkimusten kanssa näytetään että risteyskohdat pirstoutuvat matalassa lämpötilassa, jossa yksittäiset nanojohtimet vielä pysyvät kokonaisina. Simulaatioiden perusteella pirstoutuminen voidaan selittää atomien diffuusion aiheuttamalla pintaenergian minimoitumisella. Risteyskohtaan muodostuu sirpale hyvin luotettavasti

Mechanism of Spontaneous Surface Modifications on Polycrystalline Cu Due to Electric Fields

We present a credible mechanism of spontaneous field emitter formation in high electric field applications, such as Compact Linear Collider in CERN (The European Organization for Nuclear Research). Discovery of such phenomena opens new pathway to tame the highly destructive and performance limiting vacuum breakdown phenomena. Vacuum breakdowns in particle accelerators and other devices operating at high electric fields is a common problem in the operation of these devices. It has been proposed that the onset of vacuum breakdowns is associated with appearance of surface protrusions while the device is in operation under high electric field. Moreover, the breakdown tolerance of an electrode material was correlated with the type of lattice structure of the material. Although biased diffusion under field has been shown to cause growth of significantly field-enhancing tips starting from initial nm-size protrusions, the mechanisms and the dynamics of the growth of the latter have not been studied yet. In the current paper we conduct molecular dynamics simulations of nanocrystalline copper surfaces and show the possibility of protrusion growth under the stress exerted on the surface by an applied electrostatic field. We show the importance of grain boundaries on the protrusion formation and establish a linear relationship between the necessary electrostatic stress for protrusion formation and the temperature of the system. Finally, we show that the time for protrusion formation decreases with the applied electrostatic stress, we give the Arrhenius extrapolation to the case of lower fields, and we present a general discussion of the protrusion formation mechanisms in the case of polycrystalline copper surfaces.Peer reviewe

Migration barriers for surface diffusion on a rigid lattice : Challenges and solutions

Abstract Atomistic rigid lattice Kinetic Monte Carlo is an efficient method for simulating nano-objects and surfaces at timescales much longer than those accessible by molecular dynamics. A laborious part of constructing any Kinetic Monte Carlo model is, however, to calculate all migration barriers that are needed to give the probabilities for any atom jump event to occur in the simulations. One of the common methods of barrier calculations is Nudged Elastic Band. The number of barriers needed to fully describe simulated systems is typically between hundreds of thousands and millions. Calculations of such a large number of barriers of various processes is far from trivial. In this paper, we will discuss the challenges arising during barriers calculations on a surface and present a systematic and reliable tethering force approach to construct a rigid lattice barrier parameterization of face-centred and body-centred cubic metal lattices. We have produced several different barrier sets for Cu and for Fe that can be used for KMC simulations of processes on arbitrarily rough surfaces. The sets are published as Data in Brief articles and available for the use.Peer reviewe

Application of artificial neural networks for rigid lattice kinetic Monte Carlo studies of Cu surface diffusion

Kinetic Monte Carlo (KMC) is a powerful method for simulation of diffusion processes in various systems. The accuracy of the method, however, relies on the extent of details used for the parameterization of the model. Migration barriers are often used to describe diffusion on atomic scale, but the full set of these barriers may become easily unmanageable in materials with increased chemical complexity or a large number of defects. This work is a feasibility study for applying a machine learning approach for Cu surface diffusion. We train an artificial neural network on a subset of the large set of 2(26) barriers needed to correctly describe the surface diffusion in Cu. Our KMC simulations using the obtained barrier predictor show sufficient accuracy in modelling processes on the low-index surfaces and display the correct thermodynamical stability of these surfaces.Peer reviewe

The effect of heat treatment on the morphology and mobility of Au nanoparticles

This work was supported by The Centre National de la Recherche Scientifique (CNRS) of France and the French Embassy Program. The authors are also grateful for partial support by COST Action CA15216, the Estonian Science Foundation (grants PUT1689 and PUT1372), the Estonian Centre of Excellence in Zero Energy and Resource Efficient Smart Buildings and Districts, ZEBE, grant 2014-2020.4.01.15.0016 and Latvian Science Council grant lzp-2018/2-0083.In the present paper, we investigate the effect of heat treatment on the geometry and mobility of Au nanoparticles (NPs) on a Si substrate. Chemically synthesized Au NPs of diameter ranging from 5 to 27 nm were annealed at 200, 400, 600 and 800 °C for 1 h. A change in the geometry from faceted to more rounded shapes were observed with increasing annealing temperature. Kinetic Monte Carlo simulations indicate that the NPs become rounded due to the minimization of the surface area and the transition to lower energy surface types (111) and (100). The NPs were manipulated on a silica substrate with an atomic force microscope (AFM) in tapping mode. Initially, the NPs were immovable by AFM energy dissipation. However, annealed NPs became movable, and less energy was required to displace the NPs annealed at higher temperature. However, after annealing at 800 °C, the particles became immovable again. This effect was attributed to the diffusion of Au into the Si substrate and to the growth of the SiO2 layer.Centre National de la Recherche Scientifique; Latvian Council of Science lzp-2018/2-0083; Eesti Teadusfondi PUT1372,PUT1689,2014-2020.4.01.15.0016; European Cooperation in Science and Technology CA15216; Institute of Solid State Physics, University of Latvia as the Center of Excellence has received funding from the European Union’s Horizon 2020 Framework Programme H2020-WIDESPREAD-01-2016-2017-TeamingPhase2 under grant agreement No. 739508, project CAMART²https://www.beilstein-journals.org/bjnano/content/pdf/2190-4286-11-6.pd

Data sets of migration barriers for atomistic Kinetic Monte Carlo simulations of Cu self-diffusion via first nearest neighbour atomic jumps

Atomistic rigid lattice Kinetic Monte Carlo (KMC) is an efficient method for simulating nano-objects and surfaces at timescales much longer than those accessible by molecular dynamics. A laborious and non-trivial part of constructing any KMC model is, however, to calculate all migration barriers that are needed to give the probabilities for any atom jump event to occur in the simulations. We have calculated three data sets of migration barriers for Cu self-diffusion with two different methods. The data sets were specifically calculated for rigid lattice KMC simulations of copper self-diffusion on arbitrarily rough surfaces, but can be used for KMC simulations of bulk diffusion as well.Peer reviewe